CN106357313A - Method for calculating interruption probability of MIMO (Multiple Input Multiple Output) relay channel for unmanned aerial vehicle (UAV) communication - Google Patents

Abstract

The invention discloses a complete UAV (unmanned aerial vehicle) relay model which comprises two types of links, wherein one type of the links is a ground-air link from a ground station to a UAV, and a channel under the link is regarded as a Rician channel; and the other type of the links is an air-air link from a UAV to a UAV, and a channel under the link is regarded as a Rayleigh channel. Although the analysis is complicated, the relay model and a channel model can well conform to actual situations. Based on the channel model, the invention also provides a method for solving the interruption probability, and the method cannot be influenced by the channel model and is suitable for any channel model with a precondition that a channel matrix of the channel model must be known. By virtue of MATLAB (matrix laboratory) simulation, a curve of characteristic values of a channel matrix H can be obtained, then by virtue of curve fitting, a mathematical expression of the characteristic values can be obtained, and then a cumulative distribution function of the characteristic values is obtained, which is much simpler. By use of the method provided by the invention, the overall interruption probability of the two sections of the links is obtained, and the interruption probability under an actual situation is well reflected.

Description

Mimo trunk channel outage probability computational methods towards UAV Communication

Technical field

The present invention relates to unmanned plane trunking traffic technical field, more particularly, to a kind of mimo relaying towards UAV Communication Channel interruption method for calculating probability.

Background technology

By mimo Technology application in UAV Communication system, communication quality can be greatly improved, especially for unmanned plane It is used in desert to search and rescue, or situations such as battlefield prospection, needs unmanned plane to transmit multitude of video and picture in real time, therefore to unmanned Machine channel capacity and transfer rate have high requirements.At present, existing channel model mainly has Rice channel, Rayleigh channel, height This channel and nakagami-m channel etc., for the ease of analysis, existing way is essentially all by above-mentioned several channel moulds Type is incorporated in UAV Communication system, thus forming unmanned plane Rice channel, unmanned plane Rayleigh channel and unmanned plane Gauss Channel etc..

Unmanned plane as the concrete advantage of trunking traffic have following some: one is that unmanned plane is more flexible than the deployment of ground communication station Convenient, and because its lift-off is highly big, so there being bigger communication range；Two is compared to satellite communication, unmanned plane cost Very low, can relatively great amount of dispose；Three be unmanned plane compared to satellite communication, time delay is lower, and bit error rate performance is more preferable. Using unmanned plane as via node, its trunking scheme has two kinds, and one kind is to amplify-forward (af), the signal accepting is not entered Row is processed, only responsible forwarding；Another kind is decoding-forwarding (df), forwards after the signal receiving being processed again.

For the radio communication channel of time-varying, when the average channel that actual transfer rate r of communication system is less than system is held During amount c, system being capable of normal work；As r > c when, i.e. proper communication will be interrupted.Outage probability is used to weigh communication system The parameter of interrupt event occurrence frequency.Outage probability is generally relevant with the distribution of channel.For mimo system, existing much do Method is to be asked using following outage probability formula:

$p_{r_{out}}(c<r)=p_r\{{\log }_2\&lsqb;\det (i_m+\frac{snr}{n}{\mathrm{hh}}^{*})\&rsqb;<r\}$

In formula, i_mFor m rank unit matrix, snr is received signal to noise ratio；H is the channel correlation matrix of m × n；h^*It is the conjugation of h Transposition, for above-mentioned outage probability formula, most of adopted methods are to be carried out mimo channel matrix h with matrix theory Svd (singular value) decomposes, and then obtains matrix h h^*Characteristic root λ₁,λ₂,…,λ_m, and then eigenvalue is analyzed, finally Draw outage probability, also have the h h that some scholars are directed under Rice channel^*, by h h^*See and make non-central multiple wishart distribution, I.e. w=h h^*, the non-central multiple wishart distribution of wherein w obedience.Then the non-central multiple wishart distribution being directed to w matrix is special Point, carries out the mathematical derivation of some row and approximate, the finally closure expression formula of release outage probability.

As shown in Figure 1, in this model, unmanned plane via node is successively for the single-link model of unmanned plane (uav) relay system It is arranged between source node and destination node.The distance between each hop link is equal, and each parameter is identical, therefore can regard as identical Channel model, or being all Rice channel, or being all Rayleigh channel.The advantage of this model is it is only necessary to set up one Individual channel model (Rice channel or Rayleigh channel) just can analyze the characteristic of whole system；Shortcoming is not to be inconsistent with practical situation, Do not account for the difference in height between earth station and unmanned plane.

The 3-D geometric model of single unmanned plane relay system is as shown in Figure 2, as seen from the figure, total in this mobility model Both links, a up-link for source node s to uav, another downlink for uav to destination node d.In this mould In type, due to up-link with downlink symmetrically, therefore, generally only need to analyze up-link or downlink is Can.The advantage of this model is it is contemplated that the characteristic of unmanned plane practical flight, can preferably react truth, be exactly also by Symmetrical in upper and lower link, therefore only need to set up a kind of channel model.Shortcoming is that only have a frame uav in communication system, when source section When point s and destination node d wide apart, a frame uav is likely to complete relay task, now needs multi rack uav jointly complete Become relay task.

Analyzed from above, no matter being single-link model or the 3-D geometric model of unmanned plane relay system, all only Consider a kind of channel model, i.e. Rice channel or Rayleigh channel, this does not often meet the truth of unmanned plane relay system.

With matrix theory, mimo channel matrix h is carried out svd (singular value) to decompose, then obtain matrix hh^*Characteristic root λ₁,λ₂,…,λ_m, and then eigenvalue is analyzed, finally draw outage probability.The method is mainly entered to the eigenvalue of matrix It is common practice to write out the pdf (probability density function) of each eigenvalue, the pdf due to each eigenvalue is all for row analysis One extremely complex mathematic(al) representation, therefore all of eigenvalue λ₁,λ₂,…,λ_mJoint probability density function just more multiple Miscellaneous, ordinary circumstance, when eigenvalue quantity is less than or equal to 2, can be obtained with approximate method, when the quantity of eigenvalue is more than When 2, it is difficult to obtain its exact expression.In addition, different channels model, the pdf of its eigenvalue is also different, therefore the party Method be unsuitable for antenna amount more in the case of mimo channel；It is for Rice channel that another kind seeks method, by h h^*See and make Non-central multiple wishart matrix, i.e. w=h h^*, wherein w obeys non-central multiple wishart distribution, due to outage probability with The accumulative eigenvalue distribution function of wishart matrix is related, therefore can draw closing of outage probability by analysis wishart matrix Close expression formula.The method is mainly analyzed to the feature Distribution value of wishart matrix, and it substantially keeps up with states matrix decomposition and ask Method is similar, and only the method is just for Rice channel.

The method of above solution outage probability is all the feelings for channel matrix h unknown (can not obtain channel matrix) Condition, its thought is transformation assay target, and the targeted transformation that will be not easy to analyze is the target being easier to analyze.Specifically It is the analysis of unknown matrix h to be converted into the analysis to its eigenvalue and comes up.Its shortcoming except above-mentioned listed in addition to, also It is to different channels model (as Gaussian channel and Rice channel), the pdf of its eigenvalue can be very different, so different letter Road model just has different outage probabilities and seeks method, it is thus impossible to be asked in different channels model with a unified method Disconnected probability.

Content of the invention

It is an object of the invention to the advantage of comprehensive two kinds of unmanned plane relay-models of the prior art, reasonable reaction Unmanned plane relaying under truth it is proposed that a kind of multiple no-manned plane relay system model more meeting with practical situation, and The shortcoming seeking method based on outage probability of the prior art, the present invention proposes a kind of computational methods of outage probability, with one Unified method to seek the outage probability under different channels model, that is, uses the method can relay system in the hope of the multiple no-manned plane of the present invention Outage probability under the earth-to-space link of system model and the outage probability under absolutely empty link, then combine both, draw The outage probability of whole relay system.

For reaching above-mentioned purpose, the present invention is achieved through the following technical solutions:

A kind of mimo trunk channel outage probability computational methods towards UAV Communication, the mimo of described UAV Communication Trunk channel includes: vacant lot link and absolutely empty link, and wherein, vacant lot link is divided into straight length and non-straight length, looks at road straight The direct projection los component of footpath transmission signal, the non-direct projection nlos component of non-straight length transmission signal, nlos component comprises to scatter again Dif component and reflection spe component, vacant lot link channel is Rice channel, and absolutely empty link channel is Rayleigh channel；Try to achieve vacant lot The channel matrix h of link channel and absolutely empty link channel, in the case of known to channel matrix h, is drawn by matlab emulation The curve of channel matrix h eigenvalue, then passes through curve matching again, draws the mathematic(al) representation of eigenvalue, and then it is tired to obtain it Long-pending distribution function, thus obtain the outage probability under the outage probability and absolutely empty link under the link of vacant lot.

Brief description

Fig. 1 is the single-link model schematic of unmanned plane relay system；

Fig. 2 is the geometric model schematic diagram of single unmanned plane relay system；

Fig. 3 is the multiple no-manned plane relaying geometric model schematic diagram of the present invention；

Fig. 4 is unmanned plane mimo coordinate system schematic diagram；

Fig. 5 is unmanned plane mimo channel model schematic diagram；

Fig. 6 is two-dimensional geometry bicyclic mimo model schematic；

Fig. 7 is the relation (snr=20db) of the channel capacity under ground-air link and transmitting antenna spacing；

Fig. 8 is the relation (δ between channel capacity and received signal to noise ratio under ground-air link_pq=6 λ)；

Fig. 9 is the relation (δ of the channel capacity under ground-air link and the unmanned plane angle of pitch_pq=δ_nm=6 λ)；

Figure 10 is channel capacity and unmanned plane azimuthal relation (δ under ground-air link_pq=δ_nm=6 λ)；

Figure 11 is the relation (γ of the channel capacity under ground-air link and flying distance_u=α_u=0)；

Figure 12 is the relation of the channel capacity under air-air link and signal to noise ratio snr；

Figure 13 is the relation (snr=20db) of air-air link lower channel capacity and transmitting antenna spacing；

Figure 14 is the relation (snr=20db) between the channel capacity of air-air link and transmitting antenna inclination angle；

Figure 15 is under ground-air linkCurve and matched curve；

Figure 16 is under air-air linkCurve and matched curve；

Figure 17 is the outage probability curve under ground-air link；

Figure 18 is the outage probability curve under air-air link；

Figure 19 is the outage probability curve under two sections of links.

Specific embodiments

Combine accompanying drawing below by specific embodiment the present invention is described in further detail.

Traditional analysis uav relay system, or being to set up single-link model shown in accompanying drawing 1, or be shown in accompanying drawing 2 Single unmanned plane relay-model.In accompanying drawing 1, the shortcoming of model is the difference in height not accounted between earth station and uav, with actual uav Relay system is not inconsistent；In accompanying drawing 2, the shortcoming of model is that only have a frame uav between source node s and destination node d, when uav communication half Footpath is less, and when the distance between source node s and destination node d are larger, a frame uav generally can not meet communicating requirement.For Problem above, the model that the present invention is built such as accompanying drawing 3, this model had both considered the difference in height between earth station and uav, it is further contemplated that Because the distance between source node s and destination node d are excessive, a caused frame uav is it cannot be guaranteed that the problem of communication.Although this Invent built relay-model it is contemplated that two kinds of channel models, analysis is got up may be more complicated, but this relay-model and channel Model, reasonable tally with the actual situation, in addition this relay-model combine uav flight characteristics, the angle of pitch that uav is flown, The factors such as the spacing between azimuth, unmanned plane antenna are all taken into account, affect each of uav relay system than more comprehensively analyzing Plant parameter.

As shown in Figure 3, the multiple no-manned plane relay system 3-D geometric model of the present invention, can be divided into three kinds of data altogether Link, that is, source node node1 (s) arrive the air-ground up-link of uav1, the absolutely empty link of uav1 to uav2 or uav2 to uav3 with And uav3 is to the vacant lot downlink of destination node node2 (d).Source node node1 (s) is arrived to the air-ground uplink of uav1 Road, this link is divided into straight length and non-straight length, the wherein direct projection (los) of straight length transmission signal point by the present invention Amount, non-direct projection (nlos) component of non-straight length transmission signal, due to there being blocking and ground of barrier near base station Reflection, therefore, nlos component comprises to scatter (dif) component and reflection (spe) component again.Therefore this uplink channel can be regarded as Rice channel.

For the absolutely empty link of uav1 to uav2 or uav2 to uav3, due to scattering and the reflection of a large amount of particles of in the air And unmanned plane itself blocks so that this link no direct component to antenna, therefore this absolutely empty link channel can regard Rayleigh letter as Road.From above analysis it can be seen that the multiple no-manned plane relay system model set up of the present invention, reasonable react true In the case of unmanned plane relaying, more meet with practical situation.

Because air-ground up data link is symmetrical with vacant lot down data links, therefore a kind of data link can be regarded as.Therefore, Two kinds of data link of Main Analysis, i.e. ground-air up-link and air-air link, and ground-air uplink channel can regard Lai Si as Channel, air-air link channel can regard Rayleigh channel as.The present invention will make a concrete analysis of both channel models below.

First, this mimo channel of ground-air up-link Lay

In order to improve Unmanned Aerial Vehicle Data transmission capacity, the present invention adopts mimo channel, can promote taking 2 yuan of antennas as a example To multidimensional antenna.In conjunction with unmanned plane self structure, first 2 yuan of omnidirectional antennas are efficiently arranged on unmanned plane, earth station Place 2 omnidirectional antennas, set up coordinate system as shown in Figure 4.Wherein at a distance of δ, grounded receiving station is in one to unmanned plane antenna Individual radius is h for r height_c3d annulus scattering environments.X-y plane comprises with 2 yuan of grounded receiving station antenna connection midpoint o_g(high Spend for h_g) for the center of circle incisal plane, unmanned plane antenna midpoint x-y plane projection o be coordinate system initial point, connection o-o_gMake For x-axis, connect o-o_uAs z-axis；The z of unmanned plane coordinate system_uAxle is overlapped with z-axis, x_u-y_uPlane is parallel to x-y plane；Receive The x of coordinate system_gOverlap with x-axis, y_g-z_gPlane, parallel to y-z plane, so allows for launching coordinate system o_u-x_uy_uz_u, receive Coordinate system o_g-x_gy_gz_gThere is identical parallel attribute with o-xyz coordinate system

Under this coordinate system, unmanned plane body axis system o_b-x_by_bz_bIt is defined as: the center with 2 yuan of antennas of unmanned plane is Initial point o_b；x_bAxle and air speed axial direction v_uOverlap；y_bAxle (crosses x perpendicular to airframe symmetrical plane_bAxle is vertical with x-y face Plane) point to fuselage right；z_bThe vertical x of axle_bo_by_bAnd point to below fuselage.Therefore, the flight attitude angle of unmanned plane can describe For:

The angle of pitch: x_bAxle and horizontal plane x_u-y_uBetween angle γ_u, come back as just；

Roll angle: z_bAxle with by x_bAngle β between the vertical guide of axle_u, unmanned plane is tilted to the right as just；

Yaw angle (azimuth): x_bProjection on horizontal plane x-y for the axle and the angle α of x-axis_u, head right avertence navigates as just.

There is obvious difference in height for Transmitting and Receiving End, scattering object surrounding distribution centered on receiving terminal, and there is the angle of pitch During extension, " annulus " scattering model describes channel statistical feature well, and correlation measurements also demonstrate scattering object annulus The reasonability of distribution.Therefore, build based on scattering object three-dimensional geometry distribution single reflection concentric circular (gbsbcm) have direct projection, Reflection and the unmanned plane mimo mode of scattering component, as shown in Figure 5.

In accompanying drawing 5, unmanned plane antenna t_p,t_qThe angle of pitch of line and azimuth are respectively γ_uAnd α_u；Terrestrial receiving antenna r_m,r_nThe angle of pitch of line and azimuth are respectively γ_gAnd α_g；Unmanned plane horizontal flight is apart from d, flying height h_u, ground receiver Antenna space length is δ_nm, they meet d > > h_u>>r>>h_c>>h_g>>max(δ,δ_nm), s_lRepresent l-th scattering object；s_l' represent s_lProjection in receiving coordinate system.

For having n_tIndividual transmitting antenna and n_rThe mimo system of individual reception antenna, channel capacity is represented by:

$c={\log }_2\&lsqb;\det (i_{n_r}+\frac{snr}{n_t}{\mathrm{hh}}^{*})\&rsqb;(bit/s/hz)---\left(1\right)$

In formula,For n_rRank unit matrix, snr is received signal to noise ratio；H is n_t×n_rChannel correlation matrix；h^*It is h Conjugate transpose, because channel coefficients are stochastic variables, above-mentioned channel capacity is instantaneous channel capacity.Therefore, it can be gone through with each state To describe channel capacity through capacity, to obtain ergodic capacity by averaging to all of channel coefficients:

$\stackrel{\&overbar;}{c}=e_h\left(c\right)---\left(2\right)$

Understand from formula (1), obtaining channel correlation matrix h is the key trying to achieve mimo channel capacity c, due to wrapping in channel Containing direct component (los), reflecting component (spe) and certain scattering component (dif), therefore channel matrix h can be analyzed to:

H=η_losh_los+η_speh_spe+η_difh_dif(3)

η in formula_los、η_speAnd η_difBe respectively direct projection, reflection and the ratio shared in total receiving power of scattering component because Son it may be assumed that

$\left\{\begin{array}{c}{\mathrm{\&eta;}}_{los}=\sqrt{k_{rice}/(1+k_{rice}+k_{rice}{\mathrm{\&gamma;}}^2)}\\ {\mathrm{\&eta;}}_{spe}=\mathrm{\&gamma;}\sqrt{k_{rice}/(1+k_{rice}+k_{rice}{\mathrm{\&gamma;}}^2)}\\ {\mathrm{\&eta;}}_{dif}=\sqrt{1/(1+k_{rice}+k_{rice}{\mathrm{\&gamma;}}^2)}\end{array}\right.---\left(4\right)$

In formula, γ ∈ [- 1,1] is specularity factor, i.e. the ratio of incidence wave and echo；k_riceFor Rice factor, that is, The ratio of direct projection and the performance number of scattering component.

H in formula (3)_los、h_speAnd h_difRepresent the channel matrix of direct projection, reflection and scattering respectively, in 2 yuan of antennas of unmanned plane In mimo system, with direct component h_losAs a example, h_losIt is represented by:

$h_{los}=e\left\{\left[\begin{array}{cc}{h}_{np,los}(t,f)& h_{nq,los}(t,f)\\ h_{mp,los}(t,f)& h_{mq,los}(t,f)\end{array}\right]\right\}---\left(5\right)$

In formula, h_{Np, los}(t, f), h_{Nq, los}(t, f), h_{Mp, los}(t, f) and h_{Mq, los}(t, f) represents transmitting antenna to reception sky The direct component channel coefficient of line.h_speAnd h_difExpression formula and h_losSimilar, simply channel coefficients are by reflecting component and scattering The channel coefficients of component replace.Then channel coefficients are normalized, withOn the basis of, and make Use matrix h_losDivided byThe expression formula obtaining correlation matrix is:

$h_{los}=e\left\{\left[\begin{array}{cc}1& \frac{h_{nq}^{los}(t,f)}{h_{np}^{los}(t,f)}\\ \frac{h_{mp}^{los}(t,f)}{h_{np}^{los}(t,f)}& \frac{h_{mq}^{los}(t,f)}{h_{np}^{los}(t,f)}\end{array}\right]\right\}---\left(6\right)$

WithAs a example, it is represented byIts remainder, with this similar solution, finally can obtain h_los, WhereinSpace-time-frequency correlation function for direct component.Therefore formula (6) can become following formula by abbreviation:

$h_{los}=\left[\begin{array}{cc}1& \frac{r_{np,nq}^{los}(0,0)}{\mathrm{re}\left\{r_{np,nq}^{los}(0,0)\right\}}\\ \frac{r_{np,mp}^{los}(0,0)}{\mathrm{re}\left\{r_{np,mp}^{los}(0,0)\right\}}& \frac{r_{np,mq}^{los}(0,0)}{\mathrm{re}\left\{r_{np,mq}^{los}(0,0)\right\}}\end{array}\right]---\left(7\right)$

Under the conditions of wide-sense stationary uncorrelated scattering (wssus) it is assumed that terrestrial receiving antenna scattering the angle of pitch and orientation Angle pdf obeys von-mises distribution and complex parameter model, then the space-time frequency phase of above-mentioned direct component respectively Close function can be reduced to:

$r_{np,mq}^{los}(\mathrm{\&delta;}t,\mathrm{\&delta;}f)=e\left(h_{np}^{los}\right(t,f\left)h_{mq}^{los*}\right(t+\mathrm{\&delta;}t,f+\mathrm{\&delta;}f\left)\right)=e^{{\mathrm{jk}}_0(d_{np}^{los}-d_{mq}^{los})}\&times;r_{los}{e}^{{\mathrm{jf}}_{los}(\mathrm{\&delta;}t,\mathrm{\&delta;}f)}---\left(8\right)$

In the same manner, can obtain the expression formula of the space-time-frequency correlation function of scattering component:

$r_{np,mq}^{spe}(\mathrm{\&delta;}t,\mathrm{\&delta;}f)=e\left(h_{np}^{spe}\right(t,f\left)h_{mq}^{spe*}\right(t+\mathrm{\&delta;}t,f+\mathrm{\&delta;}f\left)\right){=}^{{\mathrm{jk}}_0(d_{np}^{spe}-d_{mq}^{spe})}\&times;r_{spe}{e}^{{\mathrm{jf}}_{spe}(\mathrm{\&delta;}t,\mathrm{\&delta;}f)}---\left(9\right)$

Wherein

$\begin{array}{c}{d}_{np}^{los}={\&lsqb;{(h_u+\frac{{\mathrm{\&delta;}}_{pq}}{2}{\mathrm{sin\&gamma;}}_u-h_g-\frac{{\mathrm{\&delta;}}_{nm}}{2}{\mathrm{sin\&gamma;}}_g)}^2+{(d-\frac{{\mathrm{\&delta;}}_{pq}}{2}{\mathrm{cos\&gamma;}}_u{\mathrm{cos\&alpha;}}_u+\frac{{\mathrm{\&delta;}}_{nm}}{2}{\mathrm{cos\&gamma;}}_g{\mathrm{cos\&alpha;}}_g)}^2\&rsqb;}^{1/2}\\ d_{mq}^{los}={\&lsqb;{(h_u-\frac{{\mathrm{\&delta;}}_{pq}}{2}{\mathrm{sin\&gamma;}}_u-h_g+\frac{{\mathrm{\&delta;}}_{nm}}{2}{\mathrm{sin\&gamma;}}_g)}^2+{(d+\frac{{\mathrm{\&delta;}}_{pq}}{2}{\mathrm{cos\&gamma;}}_u{\mathrm{cos\&alpha;}}_u-\frac{{\mathrm{\&delta;}}_{nm}}{2}{\mathrm{cos\&gamma;}}_g{\mathrm{cos\&alpha;}}_g)}^2\&rsqb;}^{1/2}\\ d_{np}^{spe}={\&lsqb;{(h_u+\frac{{\mathrm{\&delta;}}_{pq}}{2}{\mathrm{sin\&gamma;}}_u+h_g+\frac{{\mathrm{\&delta;}}_{nm}}{2}{\mathrm{sin\&gamma;}}_g)}^2+{(d-\frac{{\mathrm{\&delta;}}_{pq}}{2}{\mathrm{cos\&gamma;}}_u{\mathrm{cos\&alpha;}}_u+\frac{{\mathrm{\&delta;}}_{nm}}{2}{\mathrm{cos\&gamma;}}_g{\mathrm{cos\&alpha;}}_g)}^2\&rsqb;}^{1/2}\\ d_{mq}^{spe}={\&lsqb;{(h_u-\frac{{\mathrm{\&delta;}}_{pq}}{2}{\mathrm{sin\&gamma;}}_u+h_g-\frac{{\mathrm{\&delta;}}_{nm}}{2}{\mathrm{sin\&gamma;}}_g)}^2+{(d+\frac{{\mathrm{\&delta;}}_{pq}}{2}{\mathrm{cos\&gamma;}}_u{\mathrm{cos\&alpha;}}_u-\frac{{\mathrm{\&delta;}}_{nm}}{2}{\mathrm{cos\&gamma;}}_g{\mathrm{cos\&alpha;}}_g)}^2\&rsqb;}^{1/2}\end{array}---\left(10\right)$

In formula (7) and (8), k₀=2 π/λ is free space wave number, and λ is wavelength, r_losAnd r_speFor direct projection, the related letter of reflection The amplitude of number；d^losAnd d^speIt is respectively direct projection and reflection path distance between 2 antennas；f_los(δ t, δ f) and f_spe(δt,δf) It is the function with δ t and δ f as variable, and meet f_los(0,0)=f_spe(0,0)=0.

The space-time frequency function of scattering component can be reduced to:

$r_{np,mq}^{dif}(\mathrm{\&delta;}t,\mathrm{\&delta;}f)=r_{dif}{e}^{{\mathrm{jf}}_{dif}(\mathrm{\&delta;}t,\mathrm{\&delta;}f)}\&times;e^{j2{\mathrm{\&pi;k}}_0({\mathrm{cos\&gamma;}}_u{\mathrm{cos\&alpha;}}_u-{\mathrm{\&delta;}}_1{\mathrm{sin\&gamma;}}_u)/\sqrt{1+{{\mathrm{\&delta;}}_1}^2}}\&times;i_0\left(\sqrt{x^2+y^2}\right)\&times;\frac{r(m,n)}{i_0\left(k\right)}---\left(11\right)$

X=jk in formula₀δ_nmcosγ_gcosα_g+kcosθ_g0+f_x(δ t, δ f),

$y={\mathrm{jk}}_0\left(\frac{{\mathrm{\&delta;}}_{nm}{\mathrm{cos\&gamma;}}_g{\mathrm{sin\&alpha;}}_g+{\mathrm{\&delta;}}_{pq}{\mathrm{cos\&gamma;}}_u{\mathrm{sin\&alpha;}}_u{\mathrm{\&delta;}}_{xy}}{\sqrt{1+{\mathrm{\&delta;}}_1^2}}\right)+k{\mathrm{sin\&theta;}}_{g0}+f_y(\mathrm{\&delta;}t,\mathrm{\&delta;}f)$

$\begin{array}{ccc}{\mathrm{\&delta;}}_{xy}=\frac{r}{d}& {\mathrm{\&delta;}}_1=\frac{h_u-h_g-r}{d}& r(m,n)=\frac{1}{2\mathrm{\&pi;}}\end{array}$

In formula, i₀() is the 1st class zero-order Bessel (bessel) correction function；K is the angle in von-mises distribution Expand the factor；θ_g0Expand the factor for the ground receiver azimuth in the case of scattering；Obey complex parameter distributed model； r_difFor scattering the amplitude of correlation function；f_dif(δ t, δ f) is the function with δ t and δ f as variable, and meets f_dif(0,0)= 0.

Air-air link Rayleigh mimo channel

For air-air link, two frame uav are all moving, and in one plane, its mimo channel is Rayleigh channel, this Invention supposes that unmanned plane transmitting antenna and reception antenna are 2, the mimo channels of 22 receipts of composition, as a example simple analysis, false No direct projection (nlos) component between fixed two mobile unmanned planes, around antenna, the scattering object of distribution is existed with cylindric, due to nothing Difference in height very little between man-machine, therefore regarded as no difference in height, its two-dimensional geometry model is as shown in Figure 6.

It is assumed that having m and n scattering object to be centered around respectively around transmitting antenna and reception antenna, it is cylindrical in accompanying drawing 6 Being distributed in radius is r_tAnd r_rCircle on.Other each alphabetic character meanings of in figure are:Respectively it is centered around transmitting sky M around line and reception antenna and n-th scattering object；r_t、r_rIt is respectively the half of scattering object distribution transmitting antenna and reception antenna Footpath；δ_t、δ_rIt is respectively the spacing between transmitting antenna and reception antenna；v_t、v_rIt is respectively the flight speed of two frame unmanned planes；γ_t、 γ_rIt is respectively the heading (angle with x-axis) that unmanned plane sent out by two framves；θ_t、θ_rIt is respectively inclining of transmitting antenna and reception antenna Oblique angle； It is respectively the launch angle of signal and the receiving angle of signal.ε_pm、ε_mn、ε_nq, d be followed successively by transmitting antenna The distance of m-th scattering object to around transmitting antenna, around transmitting antenna, m-th scattering object dissipates for n-th to around reception antenna The distance of beam, around reception antenna, to the road distance of reception antenna, and transmitting antenna is to reception antenna for n-th scattering object Horizontal range.Wherein max { r_t,r_r< < d, max { δ_t,δ_r}<<min{r_t,r_r}；Represent transmitting antenna p, transmitting Antenna p ',Represent reception antenna q, reception antenna q '.Therefore hereinafterArriveRepresent that transmitting antenna p arrives The channel of the q ' of reception antenna,ArriveRepresent the channel of transmitting antenna p to the q of reception antenna.

For the mimo system with 2 transmitting antennas and 2 reception antennas, channel capacity is represented by:

$c={\log }_2\&lsqb;\det (i_2+\frac{snr}{2}{\mathrm{hh}}^{*})\&rsqb;(bit/s/hz)---\left(12\right)$

In formula (12), i₂For 2 rank unit matrixs, snr is received signal to noise ratio；H is 2 × 2 channel correlation matrix；h^*It is h Conjugate transpose.The expression formula of wherein channel correlation matrix is as follows:

$h=\left[\begin{array}{cc}{h}_{11}\left(t\right)& h_{12}\left(t\right)\\ h_{21}\left(t\right)& h_{22}\left(t\right)\end{array}\right]---\left(13\right)$

H in formula (13)_(·)T () represents channel coefficients, its h₁₁T () representsArriveChannel coefficients, its expression formula can Approximately it is reduced to:

$h_{11}\left(t\right)=\underset{n\&rightarrow;\mathrm{\&infin;}}{\underset{m\&rightarrow;\mathrm{\&infin;}}{\lim }}\frac{1}{\sqrt{mn}}\underset{m,n=1}{\overset{m,n}{\mathrm{\&sigma;}}}{g}_{mn}{e}^{j\&lsqb;\left(2\mathrm{\&pi;}\right(f_t^m+f_r^n)t+{\mathrm{\&theta;}}_{m,n}+{\mathrm{\&theta;}}_0)\&rsqb;}---\left(14\right)$

In formula (14), m, n are respectively centered around the number of scattering object around transmitting antenna and reception antenna,WithPoint It is not the Doppler frequency shift being caused due to the motion of transmitting antenna and reception antenna, θ_m,nFor signal dissipating around antenna The phase shift of reception antenna is reached, it is obeyed between [0,2 π] and is uniformly distributed, θ after beam₀It is a constant.Other specification is expressed Formula is as follows:

g_mn=a_mb_nc_mn(15)

$a_m=e^{j\mathrm{\&pi;}({\mathrm{\&delta;}}_t/\mathrm{\&lambda;})}cos({\mathrm{\&alpha;}}_t-{\mathrm{\&theta;}}_t)---\left(16\right)$

$b_n=e^{j\mathrm{\&pi;}({\mathrm{\&delta;}}_r/\mathrm{\&lambda;})}\cos ({\mathrm{\&alpha;}}_r-{\mathrm{\&theta;}}_r)---\left(17\right)$

$c_{mn}=e^{j\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}(r_t{\mathrm{cos\&alpha;}}_t-r_r{\mathrm{cos\&alpha;}}_r)}---\left(18\right)$

$f_t^m=f_{t_{max}}cos({\mathrm{\&alpha;}}_t-{\mathrm{\&gamma;}}_t)---\left(19\right)$

$f_r^n=f_{r_{max}}cos({\mathrm{\&alpha;}}_r-{\mathrm{\&gamma;}}_r)---\left(20\right)$

${\mathrm{\&theta;}}_0=-\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}(r_t+d+r_r)---\left(21\right)$

In above formula, λ is wavelength,It is respectively and caused due to the motion of transmitting antenna and reception antenna Maximum doppler frequency.

h₂₂T () representsArriveChannel coefficients, if a_m、b_nComplex conjugate be respectivelyBy in formula (14) A_mWithReplace, b_nWithReplace, other specification is constant, you can obtain h₂₂T the expression formula of (), in the same manner, by formula (14) a_mWithReplace, h can be obtained₁₂The expression formula of (t), and by the b in formula (14)_nWithReplace, h can be obtained₂₁T the expression formula of (), enters And the expression formula of matrix h can be drawn.

2nd, channel capacity emulation

Rice channel capacity first under emulation ground-air link, can be seen that average channel correlation matrix from formula (3) In parameter more, then affect unmanned plane mimo channel capacity many factors.In conjunction with UAV Communication environmental quality, can adopt With quantitative mode, unmanned plane mimo ergodic capacity is analyzed.It is assumed that each parameter value is as follows:

D=60km, h_u=2km, h_g=5m, h_c=300m, r=3km, θ_g0=π/8, k_rice=4db,

${\mathrm{\&gamma;}}_u={\mathrm{\&beta;}}_u={\mathrm{\&alpha;}}_u={\mathrm{\&gamma;}}_g={\mathrm{\&alpha;}}_g=\mathrm{\&pi;}/4,\mathrm{\&gamma;}=-1,k=0,{\mathrm{\&delta;}}_{nm}=10\mathrm{\&lambda;},\mathrm{\&lambda;}=\frac{c}{f}=\frac{3\&times;{10}^8(m/s)}{2\&times;{10}^{9}hz}=0.15m$

Relation first between emulation unmanned plane mimo channel capacity and unmanned plane transmitting antenna spacing, between reception antenna Away from for δ_nm=10 λ, signal to noise ratio snr=20db, its simulation result is as shown in Figure 7.Accompanying drawing 8 simulate unmanned plane channel capacity with Spacing δ between relation between reception antenna signal to noise ratio snr, wherein reception antenna_nm=6 λ.

From accompanying drawing 7: channel capacity increases with the increase of unmanned plane transmitting antenna spacing, and this is due to unmanned plane Transmitting antenna spacing is bigger, and its channel relevancy is less, then the mutual interference between channel is less, thus leading to channel capacity Increase.It can be seen that received signal to noise ratio is bigger from accompanying drawing 8, channel capacity is bigger.

Next the analysis impact to mimo channel capacity for the unmanned plane during flying attitude angle of pitch, accompanying drawing 9 and accompanying drawing 10 are respectively For the impact to mimo channel capacity of the unmanned plane angle of pitch and azimuth.

From accompanying drawing 9 it can be seen that working as unmanned plane angle of pitch γ_uWhen -50 ° about, channel capacity is maximum；Work as γ_u∈(- 90 °, -50 °) interval when, channel capacity is gradually increased；Work as γ_uWhen (- 50 °, 90 °) of ∈ is interval, channel capacity gradually decreases.Its Main cause is, the angle of pitch γ of reception antenna_g=45 °, work as γ_uWhen -45 ° about, the spatial coherence of channel is minimum, letter Road capacity is maximum, works as γ_u< when -45 °, channel relevancy is with γ_uReduction and increase, channel capacity also reduces therewith；Together should γ_u> -45 ° when, channel relevancy is with γ_uIncrease and increase, channel capacity is also with reduction.

From accompanying drawing 10, the impact to ergodic capacity for the unmanned plane azimuth symmetrically changes at 90 °, this be due to The symmetry of 2 yuan of antennas of unmanned plane, meanwhile, the position of terrestrial receiving antenna makes ergodic capacity minimum near 90 °, main Want reason to be near 90 °, receive dependency stronger.

Accompanying drawing 11 illustrates the relation of unmanned plane during flying distance and mimo channel capacity, wherein the unmanned plane during flying angle of pitch and Azimuth is 0, i.e. γ_u=α_u=0, spacing δ of reception antenna_nm=4 λ.

From accompanying drawing 11, unmanned plane during flying distance is more remote, and ergodic capacity is lower, and this is because flying distance is got over Far, space-multipath resolution capabilities are weaker, and its spatial coherence is also stronger, lead to the mutual interference of interchannel stronger, add Distance is more remote, and signal attenuation is more severe, and the signal reaching reception antenna is fewer, therefore leads to channel capacity lower.

Rayleigh channel capacity under simulated hollow-nil link below.It is assumed that d=10km, r_t=r_r=300m, λ=0.15m,

Emulate the relation of reception antenna signal to noise ratio and channel capacity first, remaining each parameter is as follows:δ_t=δ_r=10 λ, m=n=50.Its analogous diagram such as accompanying drawing 12 institute Show.As can be seen that signal to noise ratio is bigger from accompanying drawing 12, channel capacity is bigger.

Accompanying drawing 13 is the relation between transmitting antenna spacing and ergodic capacity, and remaining each parameter is:δ_r=10 λ, m=n=50.

From accompanying drawing 13, when transmitting antenna spacing δ_tWhen=4 λ, 10 λ, 16 λ, channel capacity is larger, works as δ_t=0,6 λ, 12 During λ, channel capacity is relatively small, and its reason is mainly due in δ_tWhen=4 λ, 10 λ, 16 λ, the dependency of interchannel is less, The mutual interference of interchannel is less, therefore channel capacity is larger；In δ_tWhen=0,6 λ, 12 λ, the dependency of interchannel is stronger, interchannel Mutual interference larger, therefore channel capacity is less.

Accompanying drawing 14 is the relation between transmitting antenna inclination angle and mimo ergodic capacity, and remaining each parameter is:δ_t=δ_r=10 λ, m=n=50,

From accompanying drawing 14: whenWhen, channel average size line rapidly increases, and then slowly declines one again Point, whenWhen, channel average size increases always.Its reason is, the inclination angle of reception antennaWhen When, transmitting antenna and reception antenna inclination angle contrast, therefore the signal that reception antenna receives is minimum, channel capacity is minimum, It is clear that with θ_tIncrease, channel capacity is gradually increased, untilWhen, channel capacity reaches maximum.

3rd, outage probability

The method of traditional solution outage probability, typically in the case that channel matrix h is unknown, converts thereof into and asks special The probability density function of value indicative, thus drawing the closure expression formula of outage probability, the present invention intends being asked with a unified method Outage probability under different channels model, first obtains the Rice channel used by the present invention respectively and the interruption under Rayleigh channel is general Then both combined and draw the outage probability of whole unmanned plane relay system by rate, its precondition be channel matrix h it is known that Emulated from above ergodic capacity, channel matrix h of the present invention is it is known that meet condition.Specific derivation process is as follows:

Outage probability expression formula for the mimo channel of m × n can be represented by the formula:

$p_{r_{out}}(c<r)=p_r\{{\log }_2\&lsqb;\det (i_m+\frac{snr}{n}{\mathrm{hh}}^{*})\&rsqb;<r\}---\left(22\right)$

In formula (22), c is channel capacity, and r is message transmission rate, i_mFor m rank unit matrix, snr is received signal to noise ratio； H is the channel correlation matrix of m × n；h^*It is the conjugate transpose of h.

Matrix h is crucial, h can be carried out svd decomposition with matrix analyses, i.e. h=udv^*, then have h^*=vd^*u^*, further There is hh^*=udv^*vd^*u^*=udd^*u^*, wherein u, v are unitary matrice,And λ₁,λ₂,…,λ_m For hh^*Eigenvalue.

Due to:

$\&lsqb;\det (i_m+\frac{snr}{n}{\mathrm{hh}}^{*})\&rsqb;=tr(i_m+\frac{snr}{n}{\mathrm{hh}}^{*})=\underset{i=1}{\overset{m}{\mathrm{\&pi;}}}(1+\frac{snr}{n}{\mathrm{\&lambda;}}_i)---\left(23\right)$

Formula (23) is substituted into formula (22) to be had:

$\begin{array}{c}{p}_{r_{out}}(c<r)=p_r\{{\log }_2\&lsqb;\det (i_m+\frac{snr}{n}{\mathrm{hh}}^{*})\&rsqb;<r\}\\ =p_r\{{\log }_2\underset{i=1}{\overset{m}{\mathrm{\&pi;}}}(1+\frac{snr}{n}{\mathrm{\&lambda;}}_i)<r\}\\ =p_r\{\underset{i=1}{\overset{m}{\mathrm{\&sigma;}}}{\log }_2(1+\frac{snr}{n}{\mathrm{\&lambda;}}_i)<r\}\\ =r_r\{m\underset{i=1}{\overset{m}{\mathrm{\&sigma;}}}\frac{1}{m}{\log }_2(1+\frac{snr}{n}{\mathrm{\&lambda;}}_i)<r\}\\ =p_r\{me\&lsqb;{\log }_2(1+\frac{snr}{n}\mathrm{\&lambda;})\&rsqb;<r\}\end{array}---\left(24\right)$

Had by jensen ' s inequality:

$me\&lsqb;{\log }_2(1+\frac{snr}{n}\mathrm{\&lambda;})\&rsqb;\&le;m{\log }_2(1+\frac{snr}{n}e(\mathrm{\&lambda;}\left)\right)---\left(25\right)$

Formula (25) is substituted in (24), the upper bound expression of this outage probability can be drawn, as follows:

$\begin{array}{c}{p}_{r_{out}}(c<r)=p_r\{{\log }_2(1+\frac{snr}{n}e(\mathrm{\&lambda;}\left)\right)<\frac{r}{m}\}\\ =p_r\{\left(\frac{snr}{n}e\right(\mathrm{\&lambda;}\left)\right)<2^{\frac{r}{m}}-1\}\\ =p_r\{e\left(\mathrm{\&lambda;}\right)<(2^{\frac{r}{m}}-1)\frac{n}{snr}\}\end{array}---\left(26\right)$

OrderSubstitution formula has in (26):

$p_{r_{out}}(c<r)=p_r\{\stackrel{\&overbar;}{\mathrm{\&lambda;}}<(2^{\frac{r}{m}}-1)\frac{n}{snr}\}---\left(27\right)$

Formula in (27) isThe average of eigenvalue, can be seen that, outage probability is converted into and asks by the present invention from formula (27)'s Cdf (cumulative distribution function), is emulated from above ergodic capacity, and channel matrix h of the present invention is it is known that former each of which Eigenvalue λ can be obtained, and then can obtainValue, thereforeCdf can obtain.

Ground-air link down probability

Can be seen that ergodic capacity and antenna distance δ, signal to noise ratio snr from the simulation result of accompanying drawing 7-11, uav bows Elevation angle gamma_u, azimuth angle alpha_uAnd relevant apart from d, and channel matrix h and δ, γ_u、α_uAnd d is related, thereforeWith δ, γ_u、α_u、d Correlation, i.e. δ, γ_u、α_u, the change of d will causeChange, orderRepresent eigenvalueWith the change of δ, in the same mannerRepresent eigenvalue respectivelyWith γ_u、α_u, the change of d, so δ, γ_u、α_u, the change of d The change of outage probability will be caused.Because the outage probability that different Parameters variation causes asks method similar, therefore the present invention only analyzes Apart from this parameter of d.Its concrete analysis process is as follows:

The present invention will start with from results needed below, counter push away required condition.Knowable to formula (27), obtain interrupting generally Rate, must obtain firstCdf, obtainCdf it must be understood thatExpression formula, andCurve, Ke Yiyong Matlab draws, but its accurate mathematical expression formula is difficult to obtain.In order to drawExpression formula, the present invention is in matlab The middle method of curve matching depicts a curve, and this curve can be with infinite approachReal curve, such as accompanying drawing 15 Shown.

In accompanying drawing 15, the curve with small circle isReal curve, the curve with blockage be matched curve, from In figure can be seen that, two curves almost overlap, i.e. matched curve can be regarded as and is infinitely close to real curve.Matlab can obtain The expression formula going out this matched curve is as follows:

$\stackrel{\&overbar;}{\mathrm{\&lambda;}}=\frac{29.97}{d-25.76},30\&le;d\&le;200---\left(28\right)$

In formula (28), the unit of d is km, by 30≤d≤200 it is known that,D is in [30,200] simultaneously Between obey and be uniformly distributed, that is, the cdf expression formula of d is as follows:

$f_d\left(d\right)=\frac{d}{170},30\&le;d\&le;200---\left(29\right)$

Can be obtained by formula (28), (29)Cdf expression formula as follows:

$\begin{array}{c}{f}_{\mathrm{\&lambda;}}\left(\stackrel{\&overbar;}{\mathrm{\&lambda;}}\right)=p_r\{\mathrm{\&lambda;}\&le;\stackrel{\&overbar;}{\mathrm{\&lambda;}}\}=p_r\{\frac{29.97}{d-25.76}\&le;\stackrel{\&overbar;}{\mathrm{\&lambda;}}\}\\ =p_r\{d\&greaterequal;25.76+\frac{29.97}{\stackrel{\&overbar;}{\mathrm{\&lambda;}}}\}\\ =1-p_r\{d\&le;25.76+\frac{29.97}{\stackrel{\&overbar;}{\mathrm{\&lambda;}}}\}\\ =1-\frac{1}{170}(25.76+\frac{29.97}{\stackrel{\&overbar;}{\mathrm{\&lambda;}}})\end{array}---\left(30\right)$

The outage probability expression formula that formula (30) substitution formula (27) can be obtained under ground-air link is as follows:

$\begin{array}{c}{p}_{r{1}_{out}}(c<r)=p_r\{\stackrel{\&overbar;}{\mathrm{\&lambda;}}<(2^{\frac{r}{m}}-1)\frac{n}{snr}\}=f_{\mathrm{\&lambda;}}\left(\right(2^{\frac{r}{m}}-1\left)\frac{n}{snr}\right)\\ =1-\frac{1}{170}(25.76+\frac{29.97}{(2^{\frac{r}{m}}-1)\frac{n}{snr}})\end{array}---\left(31\right)$

Air-air link down probability

The same with ground-air link down probability analysis method, channel matrix h under this air-air link and δ, θ_tAnd d phase Close, due to ground-air link analysis beDuring changeCdf, in order to keep variable consistent and seek whole system Outage probability, also analyzes hereDuring changeCdf.

Accompanying drawing 16 isReal curve and matched curve.It can be seen that after two frame uav are apart more than 5km, The average of its eigenvalue is basically unchanged, and from matlab, the expression formula of matched curve is as follows:

$\stackrel{\&overbar;}{\mathrm{\&lambda;}}=216.2d^{-4.964}+419.8,1\&le;d\&le;20---\left(32\right)$

In formula (32), the unit of d is km, by 1≤d≤20 it is known that,D takes between [1,20] simultaneously From being uniformly distributed, that is, the cdf expression formula of d is as follows:

$f_d\left(d\right)=\frac{d}{19},1\&le;d\&le;20---\left(33\right)$

Can be obtained by formula (32), (33)Cdf expression formula as follows:

$f_{\mathrm{\&lambda;}}\left(\stackrel{\&overbar;}{\mathrm{\&lambda;}}\right)=p_r\{\mathrm{\&lambda;}\&le;\stackrel{\&overbar;}{\mathrm{\&lambda;}}\}=p_r\{216.2d^{-4.934}+419.8\&le;\stackrel{\&overbar;}{\mathrm{\&lambda;}}\}$

$\begin{array}{c}=p_r\{216.2d^{-4.934}\&le;\stackrel{\&overbar;}{\mathrm{\&lambda;}}-419.8\}\\ =p_r\{d\&greaterequal;{\left(\frac{\stackrel{\&overbar;}{\mathrm{\&lambda;}}-419.8}{216.2}\right)}^{\frac{-1}{4.934}}\}\\ =1-p_r\{d\&le;{\left(\frac{\stackrel{\&overbar;}{\mathrm{\&lambda;}}-419.8}{216.2}\right)}^{\frac{-1}{4.934}}\}\\ =1-\frac{1}{19}{\left(\frac{\stackrel{\&overbar;}{\mathrm{\&lambda;}}-419.8}{216.2}\right)}^{\frac{-1}{4.934}}\end{array}---\left(34\right)$

By formula (34) substitute into formula (27) can have leisure-nil link under outage probability expression formula as follows:

$\begin{array}{c}{p}_{r{2}_{out}}(c<r)=p_r\{\stackrel{\&overbar;}{\mathrm{\&lambda;}}<(2^{\frac{r}{m}}-1)\frac{n}{snr}\}=f_{\mathrm{\&lambda;}}\left(\right(2^{\frac{r}{m}}-1\left)\frac{n}{snr}\right)\\ =1-\frac{1}{19}{\&lsqb;\frac{(2^{\frac{r}{m}}-1)\frac{n}{snr}-419.8}{216.2}\&rsqb;}^{\frac{-1}{4.934}}\end{array}---\left(35\right)$

Relay system outage probability

Analyzed by above, the present invention has obtained ground-air link and the outage probability of air-air link, below will This two sections of outage probabilities combine, and concrete analysis process is as follows:

For whole relay system, when there being a link to occur to interrupt, whole link will interrupt, only when all chains During the equal UNICOM in road, whole relay system Cai Hui UNICOM.Therefore, for ground-air link and air-air link, only this two sections During link equal energy proper communication, system just can proper communication.Because communication strategy of the present invention is, earth station will first Signal passes to uav1, after uav1 has received from the signal of earth station, is then transferred to uav2, therefore this two sections are transmitted across Journey is considered as separate, the i.e. outage probability of ground-air linkOutage probability with air-air linkMutually Independent, the outage probability expression formula that can be obtained this two sections of links by the knowledge of theory of probability is as follows:

${p_r}_{\mathrm{out}}={p_{\mathrm{rl}}}_{\mathrm{out}}+{p_{r2}}_{\mathrm{out}}-{p_{r1}}_{\mathrm{out}}\&bull;{p_{r2}}_{\mathrm{out}}---\left(36\right)$

The method of asking of outage probability of the present invention also asks method to have very big difference with conventional interrupt probability, and tradition solves outage probability Method, typically in the case that channel matrix h is unknown, converts thereof into the probability density function seeking eigenvalue, thus drawing The closure expression formula of outage probability, but for mimo channel, the probability density function of eigenvalue is generally extremely complex, has When can only be obtained with approximate method, particularly in the case that matrix dimension is higher, eigenvalue is more, its probability density letter Number is even more difficult to solve.But outage probability required by the present invention is asked in the case of known to channel matrix h, passes through Matlab emulation can draw the curve of channel matrix h eigenvalue, then passes through curve matching again it can be deduced that the mathematics of eigenvalue Expression formula, and then obtain its cumulative distribution function, do so is just simply a lot.Additionally, this outage probability seek method, be indifferent to institute Seek the property of matrix, regardless of channel, all can be asked for this method.Finally, the present invention has obtained two sections of link (i.e. ground-airs Link and air-air link) overall outage probability, the reasonable outage probability having reacted under truth.

4th, outage probability emulation

To emulate the outage probability under ground-air link first, during we draw under ground-air link by analysis before Disconnected probability expression is formula (31), that is,

$p_{r1out}=1-\frac{1}{170}(25.76+\frac{29.97}{(2^{\frac{r}{m}}-1)\frac{n}{snr}})$

The present invention built mimo channel is 2 × 2, therefore m=2, n=2, when accompanying drawing 17 simulates signal to noise ratio snr=20db Ground-air link down probabilityRelation with message transmission rate r.

Can be seen that from accompanying drawing 17, when message transmission rate r is less than 3.2 (bit/s/hz) left and right, outage probability is equal to 0, when message transmission rate r is more than 3.2 (bit/s/hz), outage probability is gradually increased, when r is 16 (bit/s/hz), Outage probability just tends towards stability.This is consistent with actual, and knowable to accompanying drawing 11, with the change apart from d, ergodic capacity exists Between [3.2,18] (bit/s/hz), therefore during r < 3.2 (bit/s/hz),During r > 16 (bit/s/hz), outage probability Tend towards stability.

Carry out the outage probability under simulated hollow-nil link below, equally, we draw air-air link by analysis before Under outage probability expression formula be formula (35), that is,

$p_{r2out}=1-\frac{1}{19}{\&lsqb;\frac{(2^{\frac{r}{m}}-1)\frac{n}{snr}-419.8}{216.2}\&rsqb;}^{\frac{-1}{4.934}}$

In the same manner, the mimo channel that the present invention is built under air-air link is 2 × 2, therefore m=2, n=2, accompanying drawing 18 simulates Air-air link down probability during signal to noise ratio snr=20dbRelation with message transmission rate r.

Can be seen that from accompanying drawing 18, when message transmission rate r is less than 11 (bit/s/hz) left and right, outage probability is equal to 0, When message transmission rate r is more than 11 (bit/s/hz), outage probability is gradually increased to tend to 1, and this is consistent with actual.From accompanying drawing Under 12 air-air link, ergodic capacity simulation result during snr=20db understands, as snr=20db, air-air link Ergodic capacity be more than 13 (bit/s/hz), therefore during r < 11 (bit/s/hz),During r > 11 (bit/s/hz), in Disconnected probability is gradually increased to close to 1, and r increases rapidly between [11,15] (bit/s/hz).

The overall outage probability of above-mentioned two sections of links can be obtained by formula (36), its analogous diagram as shown in Figure 19, in formula, m= 2, n=2, snr=20db

From accompanying drawing 19 it can be seen that as r < 11 (bit/s/hz), its outage probabilityWithIdentical, and? During r=11 (bit/s/hz), have a jump, and work as r > 11 (bit/s/hz) when,Value start to increase to from 0.92 In 1.Its reason is, when r < 11 (bit/s/hz), the outage probability under air-air linkTherefore have

As r=11 (bit/s/hz),Value be not 0, nowValue press formula (2.15) calculate；Work as r > 11 (bit/s/hz) it is that ground-air link and air-air link are all it may happen that interrupt, and ground-air link occurs the likelihood ratio interrupted relatively Greatly,Value from 0.82 start increase, along with air-air linkValue, thereforeValue from 0.92 start increase, With the increase further of r,WithValue all level off to 1, thereforeValue more approach 1.

In sum, the present invention establishes a complete uav relay-model, and this relay-model is divided into two kinds of links, and one To the ground-air link of uav, the channel under this link regards Rice channel as Zhong Shi earth station；Another kind be uav to uav sky- Nil link, the channel under this link is regarded as Rayleigh channel.Simultaneously the invention allows for a kind of new solution outage probability Method, the method is not affected by channel model it is adaptable to any channel model, but precondition is, the letter of this channel model Road matrix must be known.

Above content is to further describe it is impossible to assert with reference to specific preferred implementation is made for the present invention Being embodied as of the present invention is confined to these explanations.For general technical staff of the technical field of the invention, On the premise of present inventive concept, some simple deduction or replace can also be made, all should be considered as belonging to the present invention's Protection domain.

Claims (4)

1. a kind of mimo trunk channel outage probability computational methods towards UAV Communication it is characterised in that: described unmanned plane The mimo trunk channel of communication includes: vacant lot link and absolutely empty link, wherein, vacant lot link is divided into straight length and non-direct-view road Footpath, the direct projection los component of straight length transmission signal, the non-direct projection nlos component of non-straight length transmission signal, nlos component Comprise to scatter dif component and reflection spe component, vacant lot link channel is Rice channel, and absolutely empty link channel is believed for Rayleigh again Road；Try to achieve the channel matrix h of vacant lot link channel and absolutely empty link channel, in the case of known to channel matrix h, pass through Matlab emulation draws the curve of channel matrix h eigenvalue, then passes through curve matching again, draws the mathematical expression of eigenvalue Formula, and then obtain its cumulative distribution function, thus obtaining the outage probability under the outage probability and absolutely empty link under the link of vacant lot； Because vacant lot link and absolutely empty link are separate, then the outage probability of system is:

$p_{r_{\mathrm{out}}}=p_{{r1}_{\mathrm{out}}}+p_{{r2}_{\mathrm{out}}}-p_{{r1}_{\mathrm{out}}}\&centerdot;p_{{r2}_{\mathrm{out}}},$

Wherein,It is the outage probability of vacant lot link,It is the outage probability of absolutely empty link.

2. method according to claim 1 it is characterised in that: described vacant lot channel matrix h is decomposed into:

H=η_losh_los+η_speh_spe+η_difh_dif(1)

H in formula (1)_los、h_speAnd h_difRepresent the channel matrix of direct projection, reflection and scattering, η respectively_los、η_speAnd η_difIt is respectively straight Penetrate, reflect and scale factor that scattering component is shared in total receiving power,

That is:

$\left\{\begin{array}{c}{\mathrm{\&eta;}}_{los}=\sqrt{k_{rice}/\left(1+k_{rice}+k_{rice}{\mathrm{\&gamma;}}^2\right)}\\ {\mathrm{\&eta;}}_{spe}=\mathrm{\&gamma;}\sqrt{k_{rice}/\left(1+k_{rice}+k_{rice}{\mathrm{\&gamma;}}^2\right)}\\ {\mathrm{\&eta;}}_{dif}=\sqrt{1/\left(1+k_{rice}+k_{rice}{\mathrm{\&gamma;}}^2\right)}\end{array}\right.---\left(2\right)$

In formula (2), γ ∈ [- 1,1] is specularity factor, i.e. the ratio of incidence wave and echo；k_riceFor Rice factor, that is, directly Penetrate the ratio with the performance number of scattering component；With direct component h_losAs a example, h_losIt is represented by:

$h_{los}=e\left\{\left[\begin{array}{cc}{h}_{np,los}\left(t,f\right)& h_{nq,los}\left(t,f\right)\\ h_{mp,los}\left(t,f\right)& h_{mq,los}\left(t,f\right)\end{array}\right]\right\}---\left(3\right)$

In formula (3), h_np,los(t, f), h_nq,los(t, f), h_mp,los(t, f) and h_mq,los(t, f) represents transmitting antenna to reception sky The direct component channel coefficient of line, h_speAnd h_difExpression formula and h_losSimilar, simply channel coefficients are by reflecting component and scattering The channel coefficients of component replace；Then channel coefficients are normalized, withOn the basis of, and make Use matrix h_losDivided byThe expression formula obtaining correlation matrix is:

$h_{los}=e\left\{\left[\begin{array}{cc}1& \frac{h_{nq}^{los}\left(t,f\right)}{h_{np}^{los}\left(t,f\right)}\\ \frac{h_{mp}^{los}\left(t,f\right)}{h_{np}^{los}\left(t,f\right)}& \frac{h_{mq}^{los}\left(t,f\right)}{h_{np}^{los}\left(t,f\right)}\end{array}\right]\right\}---\left(4\right)$

WithAs a example, it is expressed asIts remainder, with this similar solution, finally can obtain h_los,

WhereinSpace-time-frequency correlation function for direct component；Therefore formula (4) abbreviation becomes following formula:

$h_{los}=\left[\begin{array}{cc}1& \frac{r_{np,nq}^{los}\left(0,0\right)}{\mathrm{re}\left\{r_{np,nq}^{los}\left(0,0\right)\right\}}\\ \frac{r_{np,mp}^{los}\left(0,0\right)}{\mathrm{re}\left\{r_{np,mp}^{los}\left(0,0\right)\right\}}& \frac{r_{np,mq}^{los}\left(0,0\right)}{\mathrm{re}\left\{r_{np,mq}^{los}\left(0,0\right)\right\}}\end{array}\right]---\left(5\right)$

Under the conditions of wide-sense stationary uncorrelated scattering it is assumed that terrestrial receiving antenna scattering the angle of pitch and azimuth probability density letter Number obeys von-mises distribution and complex parameter model respectively, then the space-time-frequency correlation function of above-mentioned direct component is reduced to:

$r_{np,mq}^{los}(\mathrm{\&delta;}t,\mathrm{\&delta;}f)=e\left(h_{np}^{los}\right(t,f\left)h_{mq}^{los*}\right(t+\mathrm{\&delta;}t,f+\mathrm{\&delta;}f\left)\right)=e^{{\mathrm{jk}}_0(d_{np}^{los}-d_{mq}^{los})}\&times;r_{los}{e}^{{\mathrm{jf}}_{los}(\mathrm{\&delta;}t,\mathrm{\&delta;}f)}$

In the same manner, can obtain the expression formula of the space-time-frequency correlation function of scattering component:

$r_{np,mq}^{spe}(\mathrm{\&delta;}t,\mathrm{\&delta;}f)=e\left(h_{np}^{spe}\right(t,f\left)h_{mq}^{spe*}\right(t+\mathrm{\&delta;}t,f+\mathrm{\&delta;}f\left)\right)=e^{{\mathrm{jk}}_0(d_{np}^{spe}-d_{mq}^{spe})}\&times;r_{spe}{e}^{{\mathrm{jf}}_{spe}\left(\mathrm{\&delta;}t,\mathrm{\&delta;}f\right)}$

Wherein,

$d_{np}^{los}={\&lsqb;{(h_u+\frac{{\mathrm{\&delta;}}_{pq}}{2}{\mathrm{sin\&gamma;}}_u-h_g-\frac{{\mathrm{\&delta;}}_{nm}}{2}{\mathrm{sin\&gamma;}}_g)}^2+{(d-\frac{{\mathrm{\&delta;}}_{pq}}{2}{\mathrm{cos\&gamma;}}_u{\mathrm{cos\&alpha;}}_u+\frac{{\mathrm{\&delta;}}_{nm}}{2}{\mathrm{cos\&gamma;}}_g{\mathrm{cos\&alpha;}}_g)}^2\&rsqb;}^{1/2}$

$d_{mq}^{los}={\&lsqb;{(h_u-\frac{{\mathrm{\&delta;}}_{pq}}{2}{\mathrm{sin\&gamma;}}_u-h_g+\frac{{\mathrm{\&delta;}}_{nm}}{2}{\mathrm{sin\&gamma;}}_g)}^2+{(d+\frac{{\mathrm{\&delta;}}_{pq}}{2}{\mathrm{cos\&gamma;}}_u{\mathrm{cos\&alpha;}}_u-\frac{{\mathrm{\&delta;}}_{nm}}{2}{\mathrm{cos\&gamma;}}_g{\mathrm{cos\&alpha;}}_g)}^2\&rsqb;}^{1/2}$

$d_{np}^{spe}={\&lsqb;{(h_u+\frac{{\mathrm{\&delta;}}_{pq}}{2}{\mathrm{sin\&gamma;}}_u+h_g+\frac{{\mathrm{\&delta;}}_{nm}}{2}{\mathrm{sin\&gamma;}}_g)}^2+{(d-\frac{{\mathrm{\&delta;}}_{pq}}{2}{\mathrm{cos\&gamma;}}_u{\mathrm{cos\&alpha;}}_u+\frac{{\mathrm{\&delta;}}_{nm}}{2}{\mathrm{cos\&gamma;}}_g{\mathrm{cos\&alpha;}}_g)}^2\&rsqb;}^{1/2}$

$d_{mq}^{spe}={\&lsqb;{(h_u-\frac{{\mathrm{\&delta;}}_{pq}}{2}{\mathrm{sin\&gamma;}}_u+h_g-\frac{{\mathrm{\&delta;}}_{nm}}{2}{\mathrm{sin\&gamma;}}_g)}^2+{(d+\frac{{\mathrm{\&delta;}}_{pq}}{2}{\mathrm{cos\&gamma;}}_u{\mathrm{cos\&alpha;}}_u-\frac{{\mathrm{\&delta;}}_{nm}}{2}{\mathrm{cos\&gamma;}}_g{\mathrm{cos\&alpha;}}_g)}^2\&rsqb;}^{1/2},$

k₀=2 π/λ is free space wave number, and λ is wavelength, r_losAnd r_speFor direct projection, reflect the amplitude of correlation function；d^losAnd d^spe It is respectively direct projection and reflection path distance between 2 antennas；f_los(δ t, δ f) and f_spe(δ t, δ f) is with δ t and δ f for becoming The function of amount, and meet f_los(0,0)=f_spe(0,0)=0.

3. method according to claim 1 it is characterised in that: described absolutely empty channel matrix h is:.

$h=\left[\begin{array}{cc}{h}_{11}\left(t\right)& h_{12}\left(t\right)\\ h_{21}\left(t\right)& h_{22}\left(t\right)\end{array}\right]---\left(6\right)$

H in formula (6)_(.)T () represents channel coefficients, its h₁₁T () representsArriveChannel coefficients, its expression formula approximately simplifies For:

$h_{11}\left(t\right)=\underset{n\&rightarrow;\mathrm{\&infin;}}{\underset{m\&rightarrow;\mathrm{\&infin;}}{\lim }}\frac{1}{\sqrt{mn}}\underset{m,n=1}{\overset{m,n}{\&sigma;}}{g}_{mn}{e}^{j\&lsqb;\left(2\mathrm{\&pi;}\right(f_t^m+f_r^n)t+{\mathrm{\&theta;}}_{m,n}+{\mathrm{\&theta;}}_0)\&rsqb;}---\left(7\right)$

In formula (7), m, n are respectively centered around the number of scattering object around transmitting antenna and reception antenna,WithBe respectively by The Doppler frequency shift causing in the motion of transmitting antenna and reception antenna, θ_m,nFor signal after the scattering object around antenna Reach the phase shift of reception antenna, it is obeyed between [0,2 π] and is uniformly distributed, θ₀It is a constant, other specification expression formula is such as Under:

g_mn=a_mb_nc_mn(8)

$a_m=e^{j\mathrm{\&pi;}({\mathrm{\&delta;}}_t/\mathrm{\&lambda;})}cos({\mathrm{\&alpha;}}_t-{\mathrm{\&theta;}}_t)---\left(9\right)$

$b_n=e^{j\mathrm{\&pi;}({\mathrm{\&delta;}}_r/\mathrm{\&lambda;})}\cos ({\mathrm{\&alpha;}}_r-{\mathrm{\&theta;}}_r)---\left(10\right)$

$c_{mn}=e^{j\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}({r_t}^{\cos }{\mathrm{\&alpha;}}_t-{r_r}^{\cos }{\mathrm{\&alpha;}}_r)}---\left(11\right)$

$f_t^m=f_{t_{max}}cos({\mathrm{\&alpha;}}_t-{\mathrm{\&gamma;}}_t)---\left(12\right)$

$f_r^n=f_{r_{max}}cos({\mathrm{\&alpha;}}_r-{\mathrm{\&gamma;}}_r)---\left(13\right)$

${\mathrm{\&theta;}}_0=-\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}(r_t+d+r_r)---\left(14\right)$

Wherein, λ is wavelength,It is respectively the maximum causing due to the motion of transmitting antenna and reception antenna Doppler frequency shift；h₂₂T () representsArriveChannel coefficients, if a_m、b_nComplex conjugate be respectivelyBy formula (7) a in_mWithReplace, b_nWithReplace, other specification is constant, that is, obtain h₂₂T the expression formula of (), in the same manner, by formula (7) A_mWithReplace, obtain h₁₂The expression formula of (t), and by the b in formula (7)_nWithReplace, h can be obtained₂₁T the expression formula of (), enters And the expression formula of matrix h can be drawn.

4. method according to claim 1 it is characterised in that: because vacant lot link and absolutely empty link are separate, be then The outage probability of system is:

$p_{r_{out}}=p_{r{1}_{out}}+p_{r{2}_{out}}-p_{r{1}_{out}}\&centerdot;p_{r{2}_{out}},$

Wherein,It is the outage probability of vacant lot link,It is the outage probability of absolutely empty link.